SOLUTION: The velocity of a particle is given by: v=1/(4cos2x) and initially the particle is at the origin. Find the total time of motion. I do not understand why the answer is 2.

Question 1142810: The velocity of a particle is given by: v=1/(4cos2x) and initially the particle is at the origin. Find the total time of motion.
I do not understand why the answer is 2.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Given a function f(x), df/dx is the rate of change of f. It is "velocity" only if f(x) is a position function that df/dx is the rate of change of position so "speed" or "velocity".
:
v = 1/(4cos2x)
:
therefore, v = dx/dt
:
dx/dt = 1/(4cos2x)
:
cos(2x) dx = dt/4
:
integrate both sides
:
t = 2 * sin(2x) +constant
:
Note integral of cos(2x) = (1/2) * sin(2x) +constant
:
initial condition is t=0, x=0
:
constant = 0
:
t = 2 * sin(2x)
:
Now, what does "total time of motion" mean?
:

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